{
 "cells": [
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-05-11T07:56:37.660893Z",
     "start_time": "2025-05-11T07:56:37.539894Z"
    }
   },
   "cell_type": "code",
   "source": [
    "%matplotlib inline\n",
    "import torch\n",
    "from torch import nn\n",
    "from d2l import torch as d2l\n",
    "\n",
    "T = 1000  # 总共产生1000个点\n",
    "time = torch.arange(1, T + 1, dtype=torch.float32)\n",
    "x = torch.sin(0.01 * time) + torch.normal(0, 0.2, (T,))\n",
    "d2l.plot(time, [x], 'time', 'x', xlim=[1, 1000], figsize=(6, 3))"
   ],
   "id": "8a40e93beb04142e",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 600x300 with 1 Axes>"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 9
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-05-11T07:56:37.722632Z",
     "start_time": "2025-05-11T07:56:37.708830Z"
    }
   },
   "cell_type": "code",
   "source": [
    "tau = 4\n",
    "features = torch.zeros((T - tau, tau))\n",
    "for i in range(tau):\n",
    "    features[:, i] = x[i: T - tau + i]\n",
    "labels = x[tau:].reshape((-1, 1))\n",
    "\n",
    "batch_size, n_train = 16, 600\n",
    "# 只有前n_train个样本用于训练\n",
    "train_iter = d2l.load_array((features[:n_train], labels[:n_train]),\n",
    "                            batch_size, is_train=True)"
   ],
   "id": "fbd40f67f914a409",
   "outputs": [],
   "execution_count": 10
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-05-11T07:56:37.737378Z",
     "start_time": "2025-05-11T07:56:37.728443Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# 初始化网络权重的函数\n",
    "def init_weights(m):\n",
    "    if type(m) == nn.Linear:\n",
    "        nn.init.xavier_uniform_(m.weight)\n",
    "\n",
    "# 一个简单的多层感知机\n",
    "def get_net():\n",
    "    net = nn.Sequential(nn.Linear(4, 10),\n",
    "                        nn.ReLU(),\n",
    "                        nn.Linear(10, 1))\n",
    "    net.apply(init_weights)\n",
    "    return net\n",
    "\n",
    "# 平方损失。注意：MSELoss计算平方误差时不带系数1/2\n",
    "loss = nn.MSELoss(reduction='none')"
   ],
   "id": "80404b23804d363a",
   "outputs": [],
   "execution_count": 11
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-05-11T07:57:03.419269Z",
     "start_time": "2025-05-11T07:56:37.831878Z"
    }
   },
   "cell_type": "code",
   "source": [
    "def train(net, train_iter, loss, epochs, lr):\n",
    "    trainer = torch.optim.Adam(net.parameters(), lr)\n",
    "    for epoch in range(epochs):\n",
    "        for X, y in train_iter:\n",
    "            trainer.zero_grad()\n",
    "            l = loss(net(X), y)\n",
    "            l.sum().backward()\n",
    "            trainer.step()\n",
    "        print(f'epoch {epoch + 1}, '\n",
    "              f'loss: {d2l.evaluate_loss(net, train_iter, loss):f}')\n",
    "\n",
    "net = get_net()\n",
    "train(net, train_iter, loss, 1000, 0.001)"
   ],
   "id": "1631d2d2e2e55579",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 1, loss: 0.539232\n",
      "epoch 2, loss: 0.247669\n",
      "epoch 3, loss: 0.116142\n",
      "epoch 4, loss: 0.070986\n",
      "epoch 5, loss: 0.062208\n",
      "epoch 6, loss: 0.060727\n",
      "epoch 7, loss: 0.060137\n",
      "epoch 8, loss: 0.059584\n",
      "epoch 9, loss: 0.059062\n",
      "epoch 10, loss: 0.058571\n",
      "epoch 11, loss: 0.058056\n",
      "epoch 12, loss: 0.057590\n",
      "epoch 13, loss: 0.057086\n",
      "epoch 14, loss: 0.056622\n",
      "epoch 15, loss: 0.056168\n",
      "epoch 16, loss: 0.055720\n",
      "epoch 17, loss: 0.055318\n",
      "epoch 18, loss: 0.054887\n",
      "epoch 19, loss: 0.054504\n",
      "epoch 20, loss: 0.054163\n",
      "epoch 21, loss: 0.053806\n",
      "epoch 22, loss: 0.053530\n",
      "epoch 23, loss: 0.053131\n",
      "epoch 24, loss: 0.052863\n",
      "epoch 25, loss: 0.052554\n",
      "epoch 26, loss: 0.052286\n",
      "epoch 27, loss: 0.052026\n",
      "epoch 28, loss: 0.051791\n",
      "epoch 29, loss: 0.051541\n",
      "epoch 30, loss: 0.051312\n",
      "epoch 31, loss: 0.051124\n",
      "epoch 32, loss: 0.050910\n",
      "epoch 33, loss: 0.050670\n",
      "epoch 34, loss: 0.050514\n",
      "epoch 35, loss: 0.050285\n",
      "epoch 36, loss: 0.050107\n",
      "epoch 37, loss: 0.049959\n",
      "epoch 38, loss: 0.049792\n",
      "epoch 39, loss: 0.049670\n",
      "epoch 40, loss: 0.049590\n",
      "epoch 41, loss: 0.049379\n",
      "epoch 42, loss: 0.049279\n",
      "epoch 43, loss: 0.049150\n",
      "epoch 44, loss: 0.049063\n",
      "epoch 45, loss: 0.049008\n",
      "epoch 46, loss: 0.048847\n",
      "epoch 47, loss: 0.048749\n",
      "epoch 48, loss: 0.048735\n",
      "epoch 49, loss: 0.048640\n",
      "epoch 50, loss: 0.048658\n",
      "epoch 51, loss: 0.048449\n",
      "epoch 52, loss: 0.048487\n",
      "epoch 53, loss: 0.048379\n",
      "epoch 54, loss: 0.048248\n",
      "epoch 55, loss: 0.048191\n",
      "epoch 56, loss: 0.048144\n",
      "epoch 57, loss: 0.048089\n",
      "epoch 58, loss: 0.047989\n",
      "epoch 59, loss: 0.047959\n",
      "epoch 60, loss: 0.047898\n",
      "epoch 61, loss: 0.047989\n",
      "epoch 62, loss: 0.047800\n",
      "epoch 63, loss: 0.047749\n",
      "epoch 64, loss: 0.047734\n",
      "epoch 65, loss: 0.047709\n",
      "epoch 66, loss: 0.047631\n",
      "epoch 67, loss: 0.047569\n",
      "epoch 68, loss: 0.047649\n",
      "epoch 69, loss: 0.047559\n",
      "epoch 70, loss: 0.047487\n",
      "epoch 71, loss: 0.047392\n",
      "epoch 72, loss: 0.047509\n",
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      "epoch 995, loss: 0.044952\n",
      "epoch 996, loss: 0.044959\n",
      "epoch 997, loss: 0.044994\n",
      "epoch 998, loss: 0.044990\n",
      "epoch 999, loss: 0.045127\n",
      "epoch 1000, loss: 0.045099\n"
     ]
    }
   ],
   "execution_count": 12
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-05-11T07:57:19.406216Z",
     "start_time": "2025-05-11T07:57:19.276005Z"
    }
   },
   "cell_type": "code",
   "source": [
    "onestep_preds = net(features)\n",
    "d2l.plot([time, time[tau:]],\n",
    "         [x.detach().numpy(), onestep_preds.detach().numpy()], 'time',\n",
    "         'x', legend=['data', '1-step preds'], xlim=[1, 1000],\n",
    "         figsize=(6, 3))"
   ],
   "id": "28c185c5c8036389",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 600x300 with 1 Axes>"
      ],
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126.560938 51.585829 \nL 127.231208 55.57699 \nL 127.566343 52.238964 \nL 127.901478 50.3998 \nL 128.236613 46.32065 \nL 128.571748 45.873103 \nL 128.906883 45.997007 \nL 129.242019 49.875596 \nL 129.577154 55.194843 \nL 129.912289 55.70766 \nL 130.247424 54.437016 \nL 130.582559 61.564321 \nL 130.917694 62.202985 \nL 131.252829 53.718607 \nL 131.587965 56.445863 \nL 131.9231 52.772838 \nL 132.258235 53.98 \nL 132.59337 54.486848 \nL 132.928505 55.717917 \nL 133.26364 55.505597 \nL 133.93391 49.540341 \nL 134.269046 59.870569 \nL 134.604181 58.168182 \nL 134.939316 70.457096 \nL 135.609586 64.077689 \nL 136.279856 62.591258 \nL 136.950127 56.938911 \nL 137.285262 62.830969 \nL 137.620397 63.520601 \nL 137.955532 59.214694 \nL 138.290667 61.32476 \nL 138.625802 67.626222 \nL 138.960938 67.912811 \nL 139.296073 73.970462 \nL 139.631208 64.62418 \nL 140.301478 53.364621 \nL 140.636613 53.996284 \nL 140.971748 62.995975 \nL 141.306883 63.676529 \nL 141.642019 57.831748 \nL 141.977154 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     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 14
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-05-11T07:57:32.791602Z",
     "start_time": "2025-05-11T07:57:32.618927Z"
    }
   },
   "cell_type": "code",
   "source": [
    "multistep_preds = torch.zeros(T)\n",
    "multistep_preds[: n_train + tau] = x[: n_train + tau]\n",
    "for i in range(n_train + tau, T):\n",
    "    multistep_preds[i] = net(\n",
    "        multistep_preds[i - tau:i].reshape((1, -1)))\n",
    "\n",
    "d2l.plot([time, time[tau:], time[n_train + tau:]],\n",
    "         [x.detach().numpy(), onestep_preds.detach().numpy(),\n",
    "          multistep_preds[n_train + tau:].detach().numpy()], 'time',\n",
    "         'x', legend=['data', '1-step preds', 'multistep preds'],\n",
    "         xlim=[1, 1000], figsize=(6, 3))"
   ],
   "id": "b273f397a0dea469",
   "outputs": [
    {
     "data": {
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     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 15
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-05-11T07:57:40.164464Z",
     "start_time": "2025-05-11T07:57:39.987413Z"
    }
   },
   "cell_type": "code",
   "source": [
    "max_steps = 64\n",
    "\n",
    "features = torch.zeros((T - tau - max_steps + 1, tau + max_steps))\n",
    "# 列i（i<tau）是来自x的观测，其时间步从（i）到（i+T-tau-max_steps+1）\n",
    "for i in range(tau):\n",
    "    features[:, i] = x[i: i + T - tau - max_steps + 1]\n",
    "\n",
    "# 列i（i>=tau）是来自（i-tau+1）步的预测，其时间步从（i）到（i+T-tau-max_steps+1）\n",
    "for i in range(tau, tau + max_steps):\n",
    "    features[:, i] = net(features[:, i - tau:i]).reshape(-1)\n",
    "\n",
    "steps = (1, 4, 16, 64)\n",
    "d2l.plot([time[tau + i - 1: T - max_steps + i] for i in steps],\n",
    "         [features[:, (tau + i - 1)].detach().numpy() for i in steps], 'time', 'x',\n",
    "         legend=[f'{i}-step preds' for i in steps], xlim=[5, 1000],\n",
    "         figsize=(6, 3))"
   ],
   "id": "f7debe5da55e90d1",
   "outputs": [
    {
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39.290395 \nL 128.205963 44.120206 \nL 128.542445 50.743998 \nL 128.878927 51.382583 \nL 129.21541 49.800314 \nL 129.551892 58.675588 \nL 129.888375 59.470884 \nL 130.224857 48.905716 \nL 130.56134 52.301829 \nL 130.897822 47.727996 \nL 131.234304 49.231215 \nL 131.570787 49.862368 \nL 131.907269 51.395356 \nL 132.243752 51.130964 \nL 132.916716 43.702731 \nL 133.253199 56.566444 \nL 133.589681 54.446547 \nL 133.926164 69.749314 \nL 134.599128 61.805359 \nL 135.272093 59.954381 \nL 135.945058 52.915798 \nL 136.281541 60.252882 \nL 136.618023 61.111646 \nL 136.954505 55.749716 \nL 137.290988 58.377275 \nL 137.62747 66.224169 \nL 137.963953 66.581044 \nL 138.300435 74.124332 \nL 138.636917 62.485877 \nL 139.309882 48.464914 \nL 139.646365 49.251493 \nL 139.982847 60.458356 \nL 140.319329 61.305816 \nL 140.655812 54.027603 \nL 140.992294 58.78245 \nL 141.665259 64.302401 \nL 142.001742 71.640812 \nL 142.338224 70.290035 \nL 142.674706 75.966309 \nL 143.011189 72.005597 \nL 143.347671 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83.548081 \nL 158.152897 94.232646 \nL 158.48938 97.804614 \nL 158.825862 97.330023 \nL 159.162345 99.629117 \nL 159.498827 101.113534 \nL 159.835309 94.427003 \nL 160.171792 100.632298 \nL 160.508274 104.041888 \nL 160.844757 105.825474 \nL 161.517721 112.676781 \nL 161.854204 112.391961 \nL 162.190686 108.70041 \nL 162.527169 101.923293 \nL 162.863651 102.454061 \nL 163.200133 105.703724 \nL 163.536616 97.466479 \nL 163.873098 107.651996 \nL 164.209581 98.510246 \nL 164.546063 92.498334 \nL 165.219028 105.603113 \nL 165.55551 111.384102 \nL 165.891993 120.735782 \nL 166.228475 117.788115 \nL 166.564958 113.087027 \nL 166.90144 115.3875 \nL 167.237922 119.860216 \nL 167.574405 126.054438 \nL 167.910887 125.960792 \nL 168.24737 124.148525 \nL 168.583852 125.208548 \nL 168.920334 124.488389 \nL 169.256817 120.462723 \nL 169.593299 119.674511 \nL 169.929782 115.985694 \nL 170.266264 107.969326 \nL 170.939229 111.095428 \nL 171.275711 116.840131 \nL 171.612194 125.626886 \nL 171.948676 125.473354 \nL 172.285159 132.658581 \nL 172.621641 133.355871 \nL 172.958123 135.225888 \nL 173.631088 132.711006 \nL 173.967571 132.492046 \nL 174.304053 131.317382 \nL 174.640535 136.643589 \nL 174.977018 122.92626 \nL 175.3135 120.882976 \nL 175.649983 124.915563 \nL 175.986465 122.300968 \nL 176.65943 142.486441 \nL 176.995912 137.043796 \nL 177.332395 137.956231 \nL 177.668877 135.788298 \nL 178.00536 135.426153 \nL 178.341842 140.493331 \nL 178.678324 132.530533 \nL 179.014807 132.422859 \nL 179.351289 127.421384 \nL 179.687772 132.919711 \nL 180.360736 130.889039 \nL 180.697219 131.997663 \nL 181.033701 131.959057 \nL 181.370184 137.540257 \nL 182.043149 143.805901 \nL 182.379631 142.063219 \nL 182.716113 143.257541 \nL 183.052596 143.770221 \nL 183.389078 142.647387 \nL 183.725561 150.922252 \nL 184.062043 146.721907 \nL 184.398525 148.735904 \nL 184.735008 153.081486 \nL 185.07149 148.208462 \nL 185.407973 150.368973 \nL 185.744455 140.806249 \nL 186.080938 148.477653 \nL 186.41742 139.658809 \nL 186.753902 144.790299 \nL 187.090385 142.798416 \nL 187.426867 141.713612 \nL 187.76335 138.663989 \nL 188.099832 140.200109 \nL 188.436314 149.25982 \nL 188.772797 148.660625 \nL 189.109279 157.261169 \nL 189.445762 153.511366 \nL 189.782244 159.596499 \nL 190.118726 157.014154 \nL 190.455209 152.306035 \nL 191.128174 153.882973 \nL 191.464656 148.623139 \nL 191.801139 154.658082 \nL 192.137621 153.53677 \nL 192.474103 150.967063 \nL 192.810586 153.809733 \nL 193.147068 152.150238 \nL 193.483551 155.374266 \nL 193.820033 155.233985 \nL 194.156515 159.419009 \nL 194.492998 161.842574 \nL 195.165963 159.706293 \nL 195.838927 151.301202 \nL 196.17541 154.683815 \nL 196.511892 153.044429 \nL 196.848375 157.661472 \nL 197.52134 153.061974 \nL 197.857822 156.273004 \nL 198.194304 156.201121 \nL 198.530787 162.612259 \nL 198.867269 162.829102 \nL 199.203752 162.542216 \nL 199.876716 155.964966 \nL 200.213199 156.838078 \nL 200.886164 154.124004 \nL 201.222646 155.667948 \nL 201.559128 147.26791 \nL 201.895611 147.205806 \nL 202.232093 152.861499 \nL 202.568576 149.589926 \nL 203.241541 158.649699 \nL 203.578023 156.498058 \nL 203.914505 161.64081 \nL 204.250988 161.032891 \nL 204.923953 150.780859 \nL 205.260435 154.576693 \nL 205.596917 145.688209 \nL 205.9334 154.194921 \nL 206.269882 151.680663 \nL 206.606365 154.322425 \nL 206.942847 158.410933 \nL 207.279329 159.10568 \nL 207.615812 159.16502 \nL 207.952294 156.949639 \nL 208.288777 159.991331 \nL 208.961742 157.589313 \nL 209.298224 156.123891 \nL 209.634706 158.197018 \nL 209.971189 158.679576 \nL 210.307671 162.17907 \nL 210.644154 162.020524 \nL 210.980636 165.96 \nL 211.317118 162.812979 \nL 211.653601 163.793406 \nL 211.990083 161.059111 \nL 212.326566 160.809171 \nL 212.663048 159.318514 \nL 212.99953 157.241757 \nL 213.336013 159.820342 \nL 213.672495 159.321397 \nL 214.008978 159.88751 \nL 214.34546 161.26309 \nL 214.681943 161.282011 \nL 215.018425 158.233848 \nL 215.354907 156.604425 \nL 215.69139 157.686473 \nL 216.027872 151.239854 \nL 216.364355 151.728227 \nL 216.700837 153.935175 \nL 217.037319 149.942013 \nL 217.373802 156.053876 \nL 217.710284 157.124592 \nL 218.046767 157.350957 \nL 218.719731 155.144623 \nL 219.056214 149.033362 \nL 219.392696 154.49369 \nL 219.729179 151.585804 \nL 220.402144 158.637367 \nL 220.738626 158.306942 \nL 221.075108 160.446615 \nL 221.411591 158.502994 \nL 221.748073 153.187347 \nL 222.084556 153.200465 \nL 222.421038 153.449405 \nL 222.75752 150.846267 \nL 223.094003 160.41959 \nL 223.430485 157.22698 \nL 223.766968 156.955136 \nL 224.10345 154.201115 \nL 224.439932 154.585218 \nL 224.776415 150.019841 \nL 225.112897 156.733762 \nL 225.785862 149.171703 \nL 226.122345 158.274631 \nL 226.458827 153.668663 \nL 226.795309 155.699596 \nL 227.131792 155.470735 \nL 227.468274 156.364448 \nL 227.804757 157.834244 \nL 228.477721 151.242955 \nL 228.814204 155.97895 \nL 229.150686 150.573941 \nL 229.487169 154.050033 \nL 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290.390485 44.263569 \nL 290.726968 41.99533 \nL 291.06345 37.03693 \nL 291.399932 56.251437 \nL 291.736415 45.859872 \nL 292.072897 52.498605 \nL 292.40938 49.544432 \nL 292.745862 45.131452 \nL 293.082345 48.399755 \nL 293.755309 44.508602 \nL 294.091792 52.967394 \nL 294.764757 45.551105 \nL 295.101239 46.919376 \nL 295.437721 44.632952 \nL 295.774204 47.460618 \nL 296.110686 51.259315 \nL 296.447169 51.179256 \nL 296.783651 53.967796 \nL 297.793098 34.587053 \nL 298.129581 31.964994 \nL 298.466063 42.304223 \nL 298.802546 35.888677 \nL 299.139028 53.47641 \nL 299.47551 43.841596 \nL 299.811993 45.612055 \nL 300.484958 30.885899 \nL 300.82144 41.605519 \nL 301.157922 45.570724 \nL 301.494405 34.456248 \nL 301.830887 38.152653 \nL 302.16737 32.389159 \nL 302.503852 36.670046 \nL 302.840334 33.454049 \nL 303.176817 41.075578 \nL 303.513299 39.577994 \nL 303.849782 29.561543 \nL 304.186264 29.9672 \nL 304.522747 35.405513 \nL 304.859229 36.20899 \nL 305.195711 41.190543 \nL 305.532194 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